Existence of positive definite solution to periodic Riccati differential equation

This paper deals with the standard periodic Riccati differential equation. A complete necessary and sufficient condition is presented for the existence of Hermitian periodic positive definite (HPPD) solution. Previously, after a proper change of basis in the state space the condition can be expressed in terms of the notions of stabilizability and detectability. Moreover, it is shown that when a HPPD solution exists, it is either unique, or else there are uncountably many such solutions. The result of the paper can be considered as a valid extension of Richardson and Kwong´s (1986) result to the periodic version